Non-fixation for biased Activated Random Walks

被引：12
|
作者：
Rolla, L. T. [1 ,2 ]
Tournier, L. [3 ]
机构：
[1] Univ Buenos Aires, Argentinian Natl Res Council, Buenos Aires, DF, Argentina
[2] NYU Shanghai, NYU ECNU Inst Math Sci, Shanghai, Peoples R China
[3] Univ Paris 13, CNRS UMR 7539, LAGA, Sorbonne Paris Cite, F-93430 Villetaneuse, France
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2018年 / 54卷 / 02期
关键词：
Interacting particle systems; Activated Random Walks; Absorbing-state; Phase transition;
D O I：
10.1214/17-AIHP827
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We prove that the model of Activated Random Walks on Z(d) with biased jump distribution does not fixate for any positive density, if the sleep rate is small enough, as well as for any finite sleep rate, if the density is close enough to 1. The proof uses a new criterion for non-fixation. We provide a pathwise construction of the process, of independent interest, used in the proof of this non-fixation criterion.
引用
收藏
页码：938 / 951
页数：14
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